correlations when observations are not independant

I have a dataset with 100 cows, 10 days per cow and feeding time and
rumination time for each hour. We want to prove that feeding time of
each hour is highly correlated with rumination time in the next 2
hours, and therefore we can predict rumination time by measuring
feeding time. I have already created the dataset such as the feeding
time for each hour is matched with the rumination time 2 hours later,
in the same row.
However, I do not think I can just correlate or regress rumination
time to feeding time using the dataset as it is, with 100*10*24
observations, since observations are not independent!!! What should I
do?

Another question: I could run proc corr or prog reg, one coefficient
is just the square root of the other... or not if I report adjusted
rsquare... Since I am not comparing models , and I have just 1
dependant and 1 independant variable, do I still have to report
adjusted rsquare? If I run proc corr, there will be not adjustment at
all...The non-adjusted indeed is higher...